On Anomalies in Orbifold Theories

TL;DR

This paper investigates gauge invariance issues in five-dimensional orbifold theories with external U(1) fields, demonstrating that anomalies are canceled by a topological Chern-Simons term generated through regularization.

Contribution

It shows how a topological Chern-Simons term cancels anomalies in orbifold theories via Pauli-Villars regularization, ensuring gauge invariance.

Findings

Anomalies in orbifold theories are canceled by Chern-Simons terms.

Regularization with Pauli-Villars fermions generates the Chern-Simons term.

Gauge invariance is restored in the presence of background gauge fields.

Abstract

We study the issue of gauge invariance in five-dimensional theories compactified on an orbifold $S^1/(\mathbb{Z}_2\times \mathbb{Z}^\prime_2)$ in the presence of an external U(1) gauge field. From the four-dimensional point We study the issue of gauge invariance in five-dimensional theories compactified on an orbifold $S^1/(\mathbb{Z}_2\times \mathbb{Z}^\prime_2)$ in the presence of an external U(1) gauge field. From the four-dimensional point of view the theory contains a tower of Kaluza-Klein Dirac fermions with chiral couplings and it looks anomalous at the quantum level. We show that this ``anomaly'' is cancelled by a topological Chern-Simons term which is generated in the effective action when the gauge theory is regularized introducing an Pauli-Villars fermion with an odd mass term. In the presence of a classical background gauge field, the fermionic current acquires a vacuum expectation value, thus generating the suitable Chern-Simons term and a gauge invariant theory.